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Lax-Wendroff solvers-based Hermite reconstruction for hyperbolic problems

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  • Li, Ang
  • Li, Jiequan

Abstract

This paper develops a new family of 2k-th order accurate Lax-Wendroff solvers-based Hermite reconstructions for hyperbolic problems systematically and implements the resulting schemes in the two-stage fourth order time-stepping framework. In order to cope with numerical difficulties around discontinuities, the WENO technology is applied and in practice a hybrid choice is made between a second order (k=1) and any other higher order Hermite reconstructions (k≥2) for efficiency. This approach unifies the Hermite-type reconstructions and the Lax-Wendroff type time discretization to form compact spacetime coupling schemes. Numerical experiments demonstrate the performance of the resulting schemes.

Suggested Citation

  • Li, Ang & Li, Jiequan, 2023. "Lax-Wendroff solvers-based Hermite reconstruction for hyperbolic problems," Applied Mathematics and Computation, Elsevier, vol. 447(C).
    • Handle: RePEc:eee:apmaco:v:447:y:2023:i:c:s009630032300084x
    DOI: 10.1016/j.amc.2023.127915
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